This paper introduces a recurrent neural network approach for predicting user lifetime value in Software as a Service (SaaS) applications. The approach accounts for three connected time dimensions. These dimensions are the user cohort (the date the user joined), user age-in-system (the time since the user joined the service) and the calendar date the user is an age-in-system (i.e., contemporaneous information).The recurrent neural networks use a multi-cell architecture, where each cell resembles a long short-term memory neural network. The approach is applied to predicting both acquisition (new users) and rolling (existing user) lifetime values for a variety of time horizons. It is found to significantly improve median absolute percent error versus light gradient boost models and Buy Until You Die models.

International Journal of Forecasting, 2024.], a generalised exponential smoothing model was proposed that is able to capture strong trends and volatility in time series. This method achieved state-of-the-art performance in many forecasting tasks, but its fitting proce dure, which is based on the NUTS sampler, is very computationally expensive. In this work, w e propose several modifications to the original model, as well as a bespoke Gibbs sampler for p osterior exploration; these changes improve sampling time by an order of magnitude, thus rendering the model much more practically relevant. The new model, and sampler, are evalu ated on the M3 dataset and are shown to be competitive, or superior, in terms of accuracy to the original method, while being substantially faster to run.

Real-world time series often exhibit complex interdependencies that cannot be captured in isolation. Global models that model past data from multiple related time series globally while producing series-specific forecasts locally are now common. However, their forecasts for each individual series remain isolated, failing to account for the current state of its neighbouring series. Multivariate models like multivariate attention and graph neural networks can explicitly incorporate inter-series information, thus addressing the shortcomings of global models. However, these techniques exhibit quadratic complexity per timestep, limiting scalability. This paper introduces the Context Neural Network, an efficient linear complexity approach for augmenting time series models with relevant contextual insights from neighbouring time series without significant computational overhead. The proposed method enriches predictive models by providing the target series with real-time information from its neighbours, addressing the limitations of global models, yet remaining computationally tractable for large datasets.

This paper describes a family of seasonal and non-seasonal time series models that can be viewed as generalisations of additive and multiplicative exponential smoothing models, to model series that grow faster than linear but slower than exponential. Their development is motivated by fast-growing, volatile time series. In particular, our models have a global trend that can smoothly change from additive to multiplicative, and is combined with a linear local trend. Seasonality when used is multiplicative in our models, and the error is always additive but is heteroscedastic and can grow through a parameter sigma. We leverage state-of-the-art Bayesian fitting techniques to accurately fit these models that are more complex and flexible than standard exponential smoothing models. When applied to the M3 competition data set, our models outperform the best algorithms in the competition as well as other benchmarks, thus achieving to the best of our knowledge the best results of per-series univariate methods on this dataset in the literature. An open-source software package of our method is available.

In this paper, we propose a new short-term load forecasting (STLF) model based on contextually enhanced hybrid and hierarchical architecture combining exponential smoothing (ES) and a recurrent neural network (RNN). The model is composed of two simultaneously trained tracks: the context track and the main track. The context track introduces additional information to the main track. It is extracted from representative series and dynamically modulated to adjust to the individual series forecasted by the main track. The RNN architecture consists of multiple recurrent layers stacked with hierarchical dilations and equipped with recently proposed attentive dilated recurrent cells. These cells enable the model to capture short-term, long-term and seasonal dependencies across time series as well as to weight dynamically the input information. The model produces both point forecasts and predictive intervals. The experimental part of the work performed on 35 forecasting problems shows that the proposed model outperforms in terms of accuracy its predecessor as well as standard statistical models and state-of-the-art machine learning models.

With large quantities of data typically available nowadays, forecasting models that are trained across sets of time series, known as Global Forecasting Models (GFM), are regularly outperforming traditional univariate forecasting models that work on isolated series. As GFMs usually share the same set of parameters across all time series, they often have the problem of not being localised enough to a particular series, especially in situations where datasets are heterogeneous. We study how ensembling techniques can be used with generic GFMs and univariate models to solve this issue. Our work systematises and compares relevant current approaches, namely clustering series and training separate submodels per cluster, the so-called ensemble of specialists approach, and building heterogeneous ensembles of global and local models. We fill some gaps in the approaches and generalise them to different underlying GFM model types. We then propose a new methodology of clustered ensembles where we train multiple GFMs on different clusters of series, obtained by changing the number of clusters and cluster seeds. Using Feed-forward Neural Networks, Recurrent Neural Networks, and Pooled Regression models as the underlying GFMs, in our evaluation on six publicly available datasets, the proposed models are able to achieve significantly higher accuracy than baseline GFM models and univariate forecasting methods.

With the advent of Big Data, nowadays in many applications databases containing large quantities of similar time series are available. Forecasting time series in these domains with traditional univariate forecasting procedures leaves great potentials for producing accurate forecasts untapped. Recurrent neural networks, and in particular Long Short-Term Memory (LSTM) networks have proven recently that they are able to outperform state-of-the-art univariate time series forecasting methods in this context, when trained across all available time series. However, if the time series database is heterogeneous accuracy may degenerate, so that on the way towards fully automatic forecasting methods in this space, a notion of similarity between the time series needs to be built into the methods. To this end, we present a prediction model using LSTMs on subgroups of similar time series, which are identified by time series clustering techniques. The proposed methodology is able to consistently outperform the baseline LSTM model, and it achieves competitive results on benchmarking datasets, in particular outperforming all other methods on the CIF2016 dataset.